The value of v which minimizes the total energy required to swim a fixed distance.
The value of v which minimizes the total energy is 7.5mi/h.
The total energy required to swim a distance of 10 mi against a current of 5 mi/h is given by,
Use a graphing calculator to draw the graph of the function E with respect to v as shown in Figure 1.
Locate the point at which local minimum occurs to find the value of v which minimizes the total energy.
The value is local minimum value if when b is near v.
From Figure (1), it is noticed that there is one local minimum between and .
Point is the lowest point. This point is the point of local minimum.
The value 4606.875 is minimum for .
Therefore, the value of v which minimizes the total energy is 7.5mi/h.
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